Mean value theorems for the double zeta-function

Abstract

We prove asymptotic formulas for mean square values of the Euler double zeta-function ${\zeta }_2(s_0,s)$, with respect to $\Im s$. Those formulas enable us to propose a double analogue of the Lindel{ö}f hypothesis.

arXiv comment23 pages

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• On Witten multiple zeta-functions associated with semisimple Lie algebras III
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Cited by in corpus (24)

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• On Witten multiple zeta-functions associated with semisimple Lie algebras III
• On Witten multiple zeta-functions associated with semisimple Lie algebras IV
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• On Witten multiple zeta-functions associated with semisimple Lie algebras V
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• Generalized multiple zeta values over number fields I
• Representation growth and representation zeta functions of groups
• Evaluation of Tornheim's type of double series
• Depth reduction of a class of Witten zeta functions
• Analytic properties of Ohno function
• Functional relations for zeta-functions of weight lattices of Lie groups of type $A_3$
• An overview and supplements to the theory of functional relations for zeta-functions of root systems
• An interpolation of Ohno's relation to complex functions